Write a module¹ peano which implements the following functions:

Name and type	Description
zero :: -> peano	Constructor for the zero of the system, i.e., returns None
succ :: peano -> peano	Constructor for the rest
zerop :: peano -> bool	Check whether the given peano object is zero (in the peano sense).2
peanop:: obj -> bool	Check whether the argument is peano.
to_int :: peano -> int	Conversion
from_int :: int -> peano	ditto
peano_add :: peano, peano -> peano	Addition
peano_mult :: peano, peano -> peano	Multiplication
peano_eq :: peano, peano -> bool	Equality

Here are the rules of the game:

1. All your functions must be recursively defined (no while, proc, whatever).
2. No use of +, -, ==, <=, and so on, in your definitions. As long as it is not numerical comparison, == is allowed.

1. If we are not already in the module business, “write a module” means create a peano.py file and define your functions there. Later on you can import your function names with from peano import peano_add, peano_mult, and so on. ↩

2. We follow the LISP convention of naming predicates by attaching a p at the end of the corresponding property. The programmatic way to inquire about someone’s mood is to apply happyp to him/her. ↩